#### Question

The nth term of a sequence is 2n + 1. The n^{th} term of a different sequence is 3n -1. Work out the three numbers that are in both sequences and between 4 and 20

For the first sequence, if 4<2n + 1<20

\dfrac{3}{2} < n <\dfrac{19}{2}=9.5

n could be 2,3,4,5,6,7,8

For the second sequence, if 4<3n -1<20

\dfrac{5}{3}< n<\dfrac{21}{3} = 7

n could be 2,3,4,5,6

Therefore when n is any numbers among 2,3,4,5,6, both sequences are between 4 and 20.